code: def calculate_regression_measures(y, y_hat, protected, privileged):
      _global_checks.global_check_import(
          "scikit-learn", "fairness in regression"
      )
      from sklearn.linear_model import LogisticRegression
  
      unique_protected = np.unique(protected)
      unique_unprivileged = unique_protected[
          unique_protected != privileged
      ]
  
      data = pd.DataFrame(
          columns=[
              "subgroup",
              "independence",
              "separation",
              "sufficiency",
          ]
      )
  
      for unprivileged in unique_unprivileged:
          # filter elements
          array_elements = np.isin(
              protected, [privileged, unprivileged]
          )
  
          y_u = (
              (y[array_elements] - y[array_elements].mean())
              / y[array_elements].std()
          ).reshape(-1, 1)
          s_u = (
              (y_hat[array_elements] - y_hat[array_elements].mean())
              / y_hat[array_elements].std()
          ).reshape(-1, 1)
  
          a = np.where(protected[array_elements] == privileged, 1, 0)
  
          p_s = LogisticRegression()
          p_ys = LogisticRegression()
          p_y = LogisticRegression()
  
          p_s.fit(s_u, a)
          p_y.fit(y_u, a)
          p_ys.fit(np.c_[y_u, s_u], a)
  
          pred_p_s = p_s.predict_proba(s_u.reshape(-1, 1))[:, 1]
          pred_p_y = p_y.predict_proba(y_u.reshape(-1, 1))[:, 1]
          pred_p_ys = p_ys.predict_proba(np.c_[y_u, s_u])[:, 1]
  
          n = len(a)
  
          r_ind = ((n - a.sum()) / a.sum()) * (
              pred_p_s / (1 - pred_p_s)
          ).mean()
          r_sep = (
              (pred_p_ys / (1 - pred_p_ys) * (1 - pred_p_y) / pred_p_y)
          ).mean()
          r_suf = (
              (pred_p_ys / (1 - pred_p_ys))
              * ((1 - pred_p_s) / pred_p_s)
          ).mean()
  
          to_append = pd.DataFrame(
              {
                  "subgroup": [unprivileged],
                  "independence": [r_ind],
                  "separation": [r_sep],
                  "sufficiency": [r_suf],
              }
          )
  
          data = pd.concat([data, to_append])
  
      # append the scale
      to_append = pd.DataFrame(
          {
              "subgroup": [privileged],
              "independence": [1],
              "separation": [1],
              "sufficiency": [1],
          }
      )
      ## TODO: this should be uncommented but adds blanks to the plots
      # data = pd.concat([data, to_append])
  
      data.index = data.subgroup
      data = data.iloc[:, 1:]
      return data
  
imports: from copy import deepcopy
  import numpy
  import pandas
  from .None import checks
  from ...None import _global_checks
  from ..._explainer import helper
  from ...model_explanations._model_performance import utils
label_desc: Use image node_id 7 for calling a global function with example usage: calculate_regression_measures(y, y_hat, protected, privileged) and returns: data